Asymptotic distributions and subsampling in spectral analysis for almost periodically correlated time series

TL;DR

This paper establishes the asymptotic distributions and subsampling consistency for spectral density and coherence measures in non-stationary, almost periodically correlated time series, under mixing and moment conditions.

Contribution

It provides the first comprehensive asymptotic distribution results and subsampling methods for spectral analysis of almost periodically correlated time series.

Findings

Spectral density estimator is asymptotically normal.

Limiting distribution of coherence magnitude is derived.

Results hold under $\\alpha$-mixing and moment conditions.

Abstract

The aim of this article is to establish asymptotic distributions and consistency of subsampling for spectral density and for magnitude of coherence for non-stationary, almost periodically correlated time series. We show the asymptotic normality of the spectral density estimator and the limiting distribution of a magnitude of coherence statistic for all points from the bifrequency square. The theoretical results hold under $\alpha$-mixing and moment conditions.